Do that on paper, graphing calculator, or wherever.
I sketced them on paper here.

I saw/thought that the max f(x) is between X=0 and x=pi/4, or between X=0deg and x=45deg.
So I tested X=35 deg on the original Eq.(i).
Then by iteration I tested X=36, X=37, X=38. It seemed that max f(x) is between x=37deg and x=38deg.
By further iteration, I found max f(X) is f(37.7deg) = 5.040289.

For the min f(x), I thought it was between X=pi and X=5pi/4, or between X=180deg and X=225deg.
By iteration I found min f(X) is f(202.3deg) = 1.408267.